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Event(s) on February 2006
- 7/2/2006
| 題目: |
The Pseudo-Transient Continuation Method for Solving Nonlinear Equations |
| 講員: |
Professor C. T. Kelley, Department of Mathematics, North Carolina State University, USA |
| 時間/地點: |
11:30 - 12:30
RRS 905
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| 摘要: |
Pseudo-transient continuation is a method for finding dynamically
stable solutions of nonlinear equations. The approach mimics
temporal integration, but uses large time steps toward the end
of avoiding the cost of a fully timeaccurate simulation. In this
talk we will compare pseudo-transient continuation to conventional
damped Newton method approaches, discuss convergence results
and time step control, and present some examples.
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- 10/2/2006
| 題目: |
Error Estimates of Binomial Tree Methods for American Option Pricing |
| 講員: |
Professor Lishang Jiang, Department of Mathematics, Tongji University, China |
| 時間/地點: |
16:00 - 17:00
FSC1217
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| 摘要: |
In this talk we like to talk about error estimates in C-norm of
BTM for American-style options such as vanilla options and jump-diffusion
models, which are based on the equivalence theorems between BTM
and the explicit finite difference methods in a critical case
for free boundary problems,.
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- 21/2/2006
| 題目: |
Numerical Study of Airflow and Pollutant Transport in Urban Street Canyons |
| 講員: |
Dr. Chun-Ho Liu, Department of Building and Real Estate, The Hong Kong Polytechnic University |
| 時間/地點: |
11:30 - 12:30
FSC 1217
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| 摘要: |
Computational fluid dynamic (CFD) techniques, including 3D large-eddy
simulation(LES) and 2D − k turbulence model, are used
to investigate the characteristic airflow and gaseous pollutant
transport in street canyons of different aspect ( b h / , building-height-tostreet-width)
ratios in this study. Airflow and pollutant transport for idealized
street canyons of aspect ratio 0.5, 1 and 2 at a Reynolds number
( Re ) of 12,000 and a Schmidt number ( Sc ) of 0.72 are considered.
When the approaching wind is perpendicular to the street axis,
both LES and − k turbulence model calculate a primary
recirculation which is confined to the street canyon and is isolated
from the free-stream flow. As a result, the pollutant removal
is accomplished solely by (vertical) turbulent transport at the
roof level. LES calculates that the pollutant removal occurs
at the leeward roof level and the retention of pollutant inside
the street canyon is more than 95%. The mean-flow properties
calculated by the − k turbulence model agree well with
the LES outputs, whereas, LES explains the detailed spatio-temporal
transport processes by turbulence. Making use of the CFD results,
the air exchange (ACH) and pollutant exchange (PCH) rates are
calculated by LES and − k turbulence model, in which
their difference in ACH rates is less than 20%. Additional CFD
results show that buoyancy-driven street-canyon flow markedly
changed the characteristic air recirculation in isothermal situations.
At sufficiently high temperature difference (between wall surfaces
and ambient), the recirculating airflow structure is no longer
isolated from the free-stream flow. Subsequently, the vertical
mean flow also contributes to the air ventilation and pollutant
dilution. The air removal is still dominated by vertical velocity
fluctuation but including buoyancy could enlarge the ACH rate
by almost a factor of 4 at large temperature difference.
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- 22/2/2006
| 題目: |
Nonparametric Transition - Based Tests for Diffusions |
| 講員: |
Dr. Peng Heng, Department of Operations Research and Financial Engineering, Princeton University, USA |
| 時間/地點: |
14:30 - 15:30
FSC1217
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| 摘要: |
We develop a specification test for the transition density of
a discretely-sampled continuous-time diffusion process, based
on a comparison of a nonparametric estimate of the transition
density or distribution function to their corresponding parametric
counterparts assumed by the null hypothesis. Using the closed
form expansions for the transition density of Ait-Sahalia (2002)
under the null parametric model and the explicit nonparametric
estimate of transition density of Fan, Yao and Tong (1996), we
are able to consider a direct comparison of the two densities
for an arbitrary specification of the null parametric model.
Using two different discrepancy measures between the null and
alternative transition density and distribution functions, we
simultaneously test the model's assumptions on the drift and
diffusion functions. Our approach does not impose the assumption
that the alternative model is a one-factor diffusion model and
allows multi-factor stochastic volatility models or any stationary
Markovian processes. We establish the asymptotic null distributions
of proposed test statistics and compute their power functions.
The finite sample properties are critically investigated via
simulation studies and are compared with the test statistic of
Hong and Li (2005).
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